Modules with Finite Submodule-Lengths

Abstract

In this paper, the concepts of submodule with finite submodule-length, and
module with finite submodule-lengths are introduced. These concepts are
generalizations of the concepts of ideal with finite ideal-length and ring with
finite ideal-length.
A submodule N of an R-module M is said to have finite submodule length
if comp(I) is finite and (M / I M)Pï‚¢ , is an Artinian and Noetherian (R / I)Pï‚¢-
module,  P = P / I , I = (N:M) and P  comp(I). An R-module M has finite
submodule-lengths if each submodule of M has finite submodule-length. The
basic results about these concepts, and some relationships between modules with
finite submodule-lengths and other classes of modules are given.